Made available in DSpace on 2016-06-02T20:15:30Z (GMT). No. of bitstreams: 1 TeseJSCN.pdf: 3751402 bytes, checksum: 010e2d53bf4276d2dd403d9304a21be6 (MD5) Previous issue date: 2004-12-10 / In this work we will study through the differential operator technique the surface effect in anisotropic spin ½ quantum Heisenberg model, through theory of effective field (EFT), of a two-spins cluster, in case of simple cubic lattice. Those systems are characterized by the existence of the surfaces, thin films and superlattice, or the bulk. Therefore, the exchange interaction, among the nearest-neighboring, depends on the position of the atoms in the lattice: with the existence of surfaces we have for atoms in those plans, exchange interactions Js and in the adjacent plans interaction J. We studied the thermodynamic properties of the quantum metamagnet for the simple cubic lattice. The limit of stability of the phase antiferromagnetic is presented for the ground state (T = 0) and the respective diagrams of phases are analyzed. With the choice of the interlayer coupling interaction different from the existent in the plane (interplane), parameter λ (interaction λJ), we analyzed the influence of the crossover in the dimensionality [2d(λ =10-5) → 3d(λ =1.0)] of the system in the thermodynamic properties with the appearance of an anomaly in magnetic susceptibility. The surface effect in the thermodynamic properties is treated taking the system on thickness film l, with exchange interactions F and AF, where in that last one we applied an external field. We observed the behavior of the thin film in function of the temperature, number of layers, magnetic field and the ratio Js/J. Changing the exchange interaction between the elements and the layers of the thin film, we characterized the system as a magnetic superlattice. We chose four arrangements in the construction of the superlattice: different inter and interlayer ferromagnetic (F) interaction, the same for antiferromagnetic (AF), alternating the layers among F, and alternating superlattice composed of F (with l1 layers) and AF (with l2 layers), where l = l1 + l2 is the thickness of the film, where we observed the influence of the change of the exchange interaction in the thermodynamic properties and in the critical properties. Several phenomena were observed, as for instance, oscillation in the magnetizations and susceptibility for layers in certain values of the temperature and coupling parameters. / Obs.:Devido a restrições dos caracteres especias, verifcar resumo em texto completo para download. Neste trabalho estudaremos através da técnica do operador diferencial o efeito de superfície no modelo de Heisenberg quântico anisotrópico de spin 1/2, via teoria de campo efetivo (EFT), num aglomerado de dois spins, para uma rede cúbica simples. Esses sistemas são caracterizados pela existência de superfícies delimitadoras, filmes finos e super-redes, ou apenas o interior do material (bulk). Portanto, a interação de troca, entre os primeiros vizinhos, depende da posição dos átomos na rede: com a existência de superfícies temos para átomos nesses planos, interações de troca Js e nos planos adjacentes (bulk) interação J. Estudamos as propriedades termodinâmicas do metamagneto quântico para a rede cúbica simples. O limite de estabilidade da fase antiferromagnética é apresentada para o estado fundamental (T = 0) e os respectivos diagramas de fases são analisados. Com a escolha de uma interação entreplanos diferente da existente nos planos (interplanos), parâmetro λ (interação λJ), analisamos a influência da mudança na dimensionalidade [quase - 2d(λ =10- 5) → 3d(λ =1.0)] do sistema nas propriedades termodinâmicas com o surgimento de uma anomalia na susceptibilidade magnética total. O efeito de superfície nas propriedades termodinâmicas é tratado tomando o sistema por um filme fino de tamanho l(no de camadas), com interações de troca F e AF, onde nesse último aplicamos um campo externo. Observamos o comportamento do filme fino em função da temperatura, número de camadas, campo magnético e a razão Js/J. Fazendo variar a interação de troca entre os constituintes e as camadas do filme fino, caracterizamos o sistema como uma super-rede magnética. Escolhemos quatro arranjos na construção das super-redes: interações ferromagnética diferentes nos planos e entreplanos, o mesmo para AF, alternando as camadas entre F e AF e um sistema cuja metade das camadas têm interação F e a outra metade AF, onde observamos a influência da mudança da interação de troca nas propriedades termodinâmicas e na criticalidade. Vários fenômenos foram observados, como por exemplo, oscilação nas magnetizações e susceptibilidade por camadas para certos valores da temperatura e parâmetros de acoplamento.

Made available in DSpace on 2016-06-02T20:16:49Z (GMT). No. of bitstreams: 1 4517.pdf: 1547785 bytes, checksum: 6effb94c4a1e222fb3264328e57ccfc6 (MD5) Previous issue date: 2012-08-16 / Financiadora de Estudos e Projetos / Recent investigations on ferromagnetic monolayers predict the existence of spinwave modes without gap in the spectrum, even in the presence of anisotropy. These excitations propagate within the domain walls that exist in the monolayer, hence in quasione- dimensional structures. They are different from the known bulk-modes whose spectrum presents anisotropy gap and whose propagation may cover all the monolayer's extension. Moreover, since they do not have gap in the spectrum, the predicted modes are not associated to an activation temperature and must influence low-temperature observable physical properties. In the present work, a theoretical study is presented for a single ferromagnetic monolayer with domain walls and the response toan oscillating magnetic field. Gapless spin-wave modes' resonances are studied in the results. / Investigações recentes em monocamadas ferromagnéticas prevêem a existência de modos de onda de spin sem gap no espectro, mesmo na presença de anisotropia. Estas excitações propagam-se no interior das paredes de domínio existentes na monocamada, portanto em estruturas quase unidimensionais. Elas distinguem-se dos modos já conhecidos cujo espectro possui gap de anisotropia e cuja propagação pode cobrir toda extensão da monocamada. Além disso, por não terem gap no espectro, os modos previstos não associam uma temperatura de ativação e devem influenciar as propriedades físicas observáveis a baixas temperaturas. Este trabalho apresenta um estudo teórico de uma monocamada ferromagnética com paredes de domínio e a resposta a um campo magnético oscilante. As ressonâncias dos modos de onda de spin sem gap são estudadas como resultado.

Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2018. / Submitted by Fabiana Santos (fabianacamargo@bce.unb.br) on 2018-09-04T17:58:17Z No. of bitstreams: 1 2018_DanielCavalcanteOliveira.pdf: 1518868 bytes, checksum: 9366ca2ecd5abe8ce9a0159e96d4d7e1 (MD5) / Approved for entry into archive by Fabiana Santos (fabianacamargo@bce.unb.br) on 2018-09-11T18:05:39Z (GMT) No. of bitstreams: 1 2018_DanielCavalcanteOliveira.pdf: 1518868 bytes, checksum: 9366ca2ecd5abe8ce9a0159e96d4d7e1 (MD5) / Made available in DSpace on 2018-09-11T18:05:39Z (GMT). No. of bitstreams: 1 2018_DanielCavalcanteOliveira.pdf: 1518868 bytes, checksum: 9366ca2ecd5abe8ce9a0159e96d4d7e1 (MD5) Previous issue date: 2018-09-03 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPQ). / Trataremos dos espaços homogêneos a dois parâmetros E(κ, τ), principalmente o grupo de Heisenberg E(0,12). Falamos sobre superfícies de ângulo constante neste grupo e sua classificação. Exibiremos também algumas ferramentas necessárias ao longo do estudo e o principal objetivo deste trabalho será demonstrar uma generalização de uma proposição no espaço Euclidiano que nos dá condições para que uma superfície de curvatura média constante homeomorfa a um disco seja totalmente umbílica. Essa generalização se dá utilizando a diferencial de Abresch-Rosenberg [1] e os pares de Codazzi ([17], [11] e [19]). / In this work, we talk about the two parameters family of homogeneous spaces E(κ, τ), putting emphasis on the Heisenberg Group E(0,12). We’ll treat the concept of constant angle surfaces in this group and its classification. Also, by exhibiting a few necessary tools along the study, we prove a possible generalization of a known proposition in the euclidean space which gives us conditions to when a constant mean curvature surface homeomorphic to a bi-dimensional disk will be totally umbilical. This proposition’s generalized version is given using the Abresch Rosenberg differential [1] and Codazzi pairs ([17], [11] e [19]).

In this thesis we deal with two problems in harmonic analysis. In the first problem we discuss weighted norm inequalities for Weyl multipliers satisfying Mauceri’s condition. As an application, we prove certain multiplier theorems on the Heisenberg group and also show in the context of a theorem of Weis on operator valued Fourier multipliers that the R-boundedness of the derivative of the multiplier is not necessary for the boundedness of the multiplier transform. In the second problem we deal with a variation of a theorem of Mauceri concerning the Lp bound-edness of operators Mwhich are known to be bounded on L2 .We obtain sufficient conditions on the kernel of the operaor Mso that it satisfies weighted Lp estimates. As an application we prove Lp boundedness of Hermite pseudo-multipliers.

Made available in DSpace on 2014-06-12T18:05:35Z (GMT). No. of bitstreams: 2 arquivo632_1.pdf: 3132391 bytes, checksum: b25862303e9c57cc119629785af995a1 (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2010 / Faculdade de Amparo à Ciência e Tecnologia do Estado de Pernambuco / Nesta dissertação investigamos o estado fundamental e as excitações de um, dois e três mágnons do modelo de Heisenberg anisotrópico definido nas cadeias AB2 e ABC com acoplamentos ferromagnético e antiferromagnético, e na presença de campo magnético. Os resultados foram obtidos através do método analítico do ansatz de Bethe e de computação numérica: algoritmo de Lanczos para diagonalização exata e grupo de renormalização da matriz densidade (para o qual adotaremos a sigla inglesa DMRG). Em particular, medidas de correlação dos mágnons permitiram classificar a natureza das excitações de dois mágnons em estendidas ou localizadas. Realizamos também um amplo estudo do diagrama de fases (campo magnético versus anisotropia) do referido modelo. As características das fases foram evidenciadas através de medidas de magnetização em função do campo magnético, onde identificamos a existência das seguintes fases: crítica, paramagnética quântica, Lieb-ferrimagnética, Ising-antiferromagnética e -ferromagnética (com polarização total de spin). As referidas fases estão separadas por linhas de pontos críticos de condensação de mágnons, e por pontos multicríticos de Heisenberg e de Kosterlitz-Thouless

We investigate the quantum dynamics of the spins on different Heisenberg antiferromagnetic spin lattice systems. Firstly, we applied the coupled-cluster method to the spin-1/2 antiferromagnetic XXZ model on a square lattice by employing an approximation which contains two-body long-range correlations and high-order four-body local correlations. Improvement is found for the ground-state energy, sublattice magnetization, and the critical anisotropy when comparing with the approximation including the two-body correlations alone. We also obtain the full excitation spectrum which is in good agreement with the quantum Monte Carlo results and the high-order spin-wave theory. Secondly, we study the longitudinal excitations of quantum antiferromagnets on a triangular lattice by a recently proposed microscopic many-body approach based on magnon-density waves. We calculate the full longitudinal excitation spectra of the antiferromagnetic Heisenberg model for a general spin quantum number in the isotropic limit. Similar to the square lattice model, we find that, at the center of the first hexagonal Brillouin zone Γ(q=0) and at the magnetic ordering wavevectors ±[Q= (4π/3,0)], the excitation spectra become gapless in the thermodynamic limit, due to the slow, logarithmic divergence of the structure factor. However, these longitudinal modes on two-dimensional models may be considered as quasi-gapped, as any finite-size effect or small anisotropy will induce a large energy gap, when compared with the counterpart of the transverse spin-wave excitations. We have also investigated the excited states of the quasi-one-dimensional quantum antiferromagnets on hexagonal lattices, including the longitudinal modes based on the magnon-density waves. A model Hamiltonian with a uniaxial single-ion anisotropy is first studied by a spin-wave theory based on the one-boson method; the ground state thus obtained is employed for the study of the longitudinal modes. The full energy spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We have found two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. The excitation energy gaps due to the anisotropy and the energy gaps of the longitudinal modes without anisotropy are then investigated. We then compares our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and we find good agreements after the higher-order contributions are included in our calculations.

We start with the recollection of basic results about differential manifolds and Lie groups. We also recall some preliminary terminologies in Lie algebra. Then we define the Lie algebra corresponding to a Lie group. In the next section, we define a strongly continuous representation of a Lie group on a Banach space. We further define the smooth, analytic and entire vectors for a given representation. Then, we move on to develop some necessary and sufficient criteria to characterize smooth, analytic and entire vectors. We, in particular, take into account of some specific representations of Lie groups like the regular representation of R, the irreducible representations of Heisenberg groups, the irreducible representations of the group of Affine transformations and finally the representations of non-compact simple Lie groups.

The spin-lattice coupling is due to itinerant electrons interacting with both spins of ions and phonons, mediating a coupling between magnetic spin moments and lattice vibrations. In this project, the coupling is studied systematically for finite quantum spin chains of size 2 – 10. The coupling is included in a Hamiltonian model with the Heisenberg exchange interaction and an external magnetic field resulting in an eigenvalue problem which is solved numerically to find phase diagrams of the magnetic moment of the system depending on an external magneticfield and the lattice vibration parameter. The eigenvalue problem is also solved analytically for the 2-ion chain, dimer, and 3-ion chain, trimer, systems. Based on these phase diagrams two propositions are made: the effect of the coupling is larger than an external magnetic field and the behavior of the coupling converges to a common phase diagram for larger spin chains. / Kopplade spinn- och vibrationsfrihetersgrader beror på kringvandrande elektroner som växelverkar med både spin och fononer, vilket förmedlar en koppling mellan magnetiskt spinmoment och gittervibrationer. I detta projekt studeras denna koppling systematiskt för ändliga spin-kedjor av 2–10 joner. Systemet beskrivs av en Hamiltonian med Heisenberg modellen som beskriver spin-spin kopplingen samt ett externt magnetiskt fält. Detta egenvärdesproblem löses analytiskt för dimer- och trimersystem samt numeriskt för längre kedjor. Lösningarna används för att ta fram fasdiagram av de magnetiska momenten av kedjorna beroende på externt magnetfält och spin- och vibrationsfrihetsgradsparametern. Baserat på dessa fasdiagram, framförs två propositioner: kopplingens effekt är större än ett externt magnetfält och kopplingens beteende konvergerar till ett enhetligt fasdiagram för större spinnkedjor. / <p>Subject reader/ämnesgranskare: Anders Bergman</p>

Magnetic frustration is a phenomenon arising in spin systems when spin interactions cannot all be satisfied at the same time. A typical example of geometric frustration is a triangle with Ising-spins at its vertices and antiferromagnetic interaction. While we can easily anti-align two neighbouring spins, it is not possible for the third one to simultaneously anti-align with both of them. Another flavour of magnetic frustration is the so called exchange frustration, where different spin components interact in an Ising fashion on different bonds. Moreover, frustrated spin systems give rise to exotic states of matter, such as spin liquids, spin ices and nematic phases. As frustrated systems are rarely analytically solvable, numerical techniques are of the utmost importance in this framework. This dissertation is concerned with a specific class of models, namely one- and quasi-one-dimensional spin systems and studies their properties by making use of the density matrix renormalisation group technique. This method has been shown to be extremely powerful and reliable to study chain and ladder models. We consider examples of both geometric and exchange frustration. For the former, we take into consideration one of the prototypical examples of geometric frustration in one dimension: the J1-J2 model with ferromagnetic nearest-neighbour interaction J1<0 and antiferromagnetic next-nearest-neighbour interaction J2>0. Our results show the existence of a Haldane gap supported by a special AKLT-like valence bond solid state in a specific region of the coupling ratio. Furthermore, we consider the effect of dimerisation of the first-neighbour coupling. This dimerisation affects the critical point and the ground state underlying the spin gap. These models are of interest in the context of cuprate chain materials such as LiVCuO4, LiSbCuO4 and PbCuSO4(OH)2. Concerning exchange frustration, we consider the celebrated Kitaev-Heisenberg model: it is an extension of the exactly solvable Kitaev model with an additional Heisenberg interaction. The Kitaev-Heisenberg model is currently the minimal model for candidate Kitaev materials. The extended model is not analytically solvable and numerics are needed to study the properties of the system. While both the original Kitaev and the Kitaev-Heisenberg models live on a honeycomb lattice, we here perform systematic studies of the Kitaev-Heisenberg chain and of the two-legged ladder. While the chain cannot support a Kitaev spin liquid state, it shows nevertheless a rich phase diagram despite being a one-dimensional system. The long-range ordered states of the honeycomb can be understood in terms of coupled chains within the Kitaev-Heisenberg model. Following this reasoning, we turn our attention to the Kitaev-Heisenberg model on a two-legged ladder. Remarkably, the phase diagram of the ladder is extremely similar to that of the honeycomb model and the differences can be explained in terms of the different dimensionalities. In particular, the ladder exhibits a topologically non-trivial phase with no long-range order, i.e., a spin liquid. Finally, we investigate the low-lying excitations of the Kitaev-Heisenberg model for both the chain and the ladder geometry.

We define a faithful linear monoidal functor from the partition category, and hence from Deligne's category Rep(S_t), to the additive Karoubi envelope of the Heisenberg category. We show that the induced map on Grothendieck rings is injective and corresponds to the Kronecker coproduct on symmetric functions. We then generalize the above results to any group G, the case where G is the trivial group corresponding to the case mentioned above. Thus, to every group G we associate a linear monoidal category Par(G) that we call a group partition category. We give explicit bases for the morphism spaces and also an efficient presentation of the category in terms of generators and relations. We then define an embedding of Par(G) into the group Heisenberg category associated to G. This embedding intertwines the natural actions of both categories on modules for wreath products of G. Finally, we prove that the additive Karoubi envelope of Par(G) is equivalent to a wreath product interpolating category introduced by Knop, thereby giving a simple concrete description of that category.